Advances in Chemical Engineering by David H. West and Gregory Yablonsky (Eds.)

By David H. West and Gregory Yablonsky (Eds.)

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It is obviously most expedient to set thermodynamic constraints on individual stages as applied to fast variables whose formation to a great extent determines further course of the process studied. For example, the fast formation of harmful substances can complicate the production of target products. Derivation of formulae for additional thermodynamic con­ straints disregarding the permissible time of chemical reactions and trans­ fer processes narrows the area of effective application of the given approach.

In the work by Gorban (1984) according to Boltzmann it was supposed that this function possessed the properties of the Lyapunov functions. We will explain this method on the example of setting the constraint on the rate of the i-th chemical reaction. Let the rate equation of this reaction have the form: wi ¼ dxi  ¼ ki # xj j ; d j ð46Þ where k—the rate constant. Independence of the right-hand side of Equation (46) from  makes possible the transformation (47) and the Equilibrium Thermodynamic Modeling of Dissipative Macroscopic Systems 31 representation of derivative of the characteristic function (48) with respect to time in the form (49): 0  ki # xj j j !

It shows a scheme of the main double-pipe water heat network of the heat supply system for a large urban district. The optimal synthesis problem for this network consists in the determination of flow distribution 1 2 3 4 5 Figure 9 The scheme of heat supply system in a “double-line” representation 1, 2—sections of supply and return pipelines, 3—heat source, 4—nodes of consumer connection; 5—pumping station. M. Kaganovich et al. over the scheme branches (the zero-flow branches are excluded from the scheme) and pipeline diameters.

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